Tessellation

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries.

A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semi-regular tilings with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern. In the geometry of higher dimensions, a space-filling or honeycomb is also called a tessellation of space.

A real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor or wall coverings. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the decorative tiling of the Alhambra palace. In the twentieth century, the work of M. C. Escher often made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, for artistic effect. Tessellations are sometimes employed for decorative effect in quilting. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.

Tessellate (song)

"Tessellate" is a song by English indie rock band alt-J from their debut studio album, An Awesome Wave (2012). The song was written by Joe Newman, Gus Unger-Hamilton, Gwilym Sainsbury and Thom Green and produced by Charlie Andrew. It was released on 13 July 2012 as the album's third single. "Tessellate" has been used on television series such as CSI: NY, Longmire, and Sons of Anarchy.

In 2013, "Tessellate" was covered by English singer and songwriter Ellie Goulding on the deluxe edition of Halcyon Days, the reissue of her second studio album, Halcyon. English indie folk band Mumford & Sons also covered the song on BBC Radio 1's Live Lounge on 25 September 2012; their version was included on the compilation album BBC Radio 1's Live Lounge 2013.

Music video

A music video to accompany the release of "Tessellate" was first released on YouTube on 9 July 2012. The video was directed by Ben Newbury and is an artistic reworking of the famous painting The School of Athens by Raphael, using 21st century characters in a room similar to the painting's background (Panthéon, in Paris).